Mathmethods formula PDF

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Victorian Certificate of Education Year

MATHEMATICAL METHODS Written examinations 1 and 2

FORMULA SHEET

Instructions This formula sheet is provided for your reference.

Students are NOT permitted to bring mobile phones and/or any other unauthorised electronic devices into the examination room.

© VICTORIAN CURRICULUM AND ASSESSMENT AUTHORITY 2016 Version 2 – April 2016

MATHMETH EXAM

2

Mathematical Methods formulas Mensuration area of a trapezium

1 (a + b ) h 2

curved surface area of a cylinder

2π

volume of a cylinder

π  r   2h

volume of a cone

1 2 πr h 3

1 Ah 3

volume of a pyramid

4 3 volume πofr a sphere 3

  rh

1 bc sin ( A) 2

area of a triangle

Calculus d n x = nx n − 1 dx

∫

d n −1 (ax + b )n = an( ax + b) dx

∫ ( ax + b) dx = a(n + 1) (ax + b)

d ax e = ae ax dx

∫e

( )

(

)

( )

x n dx =

1 n+1 + c, n ≠ −1 x n +1 1

n

ax

dx =

n +1

+ c, n ≠ − 1

1 ax e +c a

1 dx = loge ( x) + c, x > 0 x

1 d ( loge (x )) = x dx

∫

d ( sin (ax )) = a cos( ax) dx

∫sin (ax)dx = − a cos (ax) + c

d ( cos ( ax)) = − a sin ( ax) dx

∫cos (ax)dx = a sin (ax) + c

1

1

a d 2 = a sec (ax ) ( tan (ax )) = 2 dx cos (ax )

product rule

d dv du ( uv) = u + v dx dx dx

chain rule

dy dy du = dx du dx

quotient rule

d  u  = dx  v 

v

du dv −u dx dx 2 v

3

MATHMETH EXAM

Probability Pr(A ∪ B) = Pr(A) + Pr(B) – Pr(A ∩ B)

Pr(A) = 1 – Pr(A′) Pr(A|B) =

Pr ( A ∩ B) Pr( B)

µ = E(X)

mean

var(X) = σ 2 = E((X – µ )2) = E(X 2) – µ2

variance

Probability distribution discrete

Pr(X = x) = p(x)

continuous

Pr(a < X < b) =

Mean

Variance

µ = ∑ x p(x)

∫

b

f ( x )dx a

µ=

∫

σ 2 = ∑ (x – µ )2 p(x)

∞

x f ( x )dx

−∞

σ2=

∫

∞

( x − µ ) 2 f ( x) dx

−∞

Sample proportions P =

X n

standard deviation

mean

ˆ)= sd ( P

p (1 − p ) n

approximate confidence interval

E(P ) = p  pˆ( 1 − pˆ) pˆ ( 1 − pˆ ) , pˆ + z  pˆ − z  n n 

END OF FORMULA SHEET

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